An example of an asymptotically Hilbertian space which fails the approximation property
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Following Davic's example of a Danach space failing the approximation property (1973), we show how to construct a Danach space E which is asymptotically Hilbcrtian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is "almost" a weak Hubert space and which can be written as the direct sum of two subspaces all of whose subspaccs have the approximation property. © 2001 P. G. Casazza, C. L. Garcia, and W. B. Johnson.
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Casazza, P. G., Garca, C. L., & Johnson, W. B.
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Casazza, PG||García, CL||Johnson, WB
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Approximation Property
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Asymptotically Hilbertian
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Banach Spaces
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Weak Hilbert Spaces
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